Quantum cryptography: Security criteria reexamined

Kaszlikowski, Dagomir; Gopinathan, Ajay; Liang, Yeong-Cherng; Kwek, Leong Chuan; Englert, Berthold-Georg

doi:10.1103/physreva.70.032306

Cited by 11 publications

(13 citation statements)

References 17 publications

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“…Measurements for such symmetrical states exist, and it is known that the error-minimizing measurement for such states is the square-root measurement [24][25][26][27][28][29]. The following results for the tomographic protocol were derived in [39,40]:…”

Section: Evaluation Of the Guessing Probabilitymentioning

confidence: 99%

Min-entropy and quantum key distribution: Nonzero key rates for “small” numbers of signals

et al. 2011

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We calculate an achievable secret key rate for quantum key distribution with a finite number of signals, by evaluating the min-entropy explicitly. The min-entropy can be expressed in terms of the guessing probability, which we calculate for d-dimensional systems. We compare these key rates to previous approaches using the von Neumann entropy and find non-zero key rates for a smaller number of signals. Furthermore, we improve the secret key rates by modifying the parameter estimation step. Both improvements taken together lead to non-zero key rates for only 10 4 − 10 5 signals. An interesting conclusion can also be drawn from the additivity of the min-entropy and its relation to the guessing probability: for a set of symmetric tensor product states the optimal minimum-error discrimination (MED) measurement is the optimal MED measurement on each subsystem.

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Section: Evaluation Of the Guessing Probabilitymentioning

confidence: 99%

Min-entropy and quantum key distribution: Nonzero key rates for “small” numbers of signals

et al. 2011

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“…For acute pyramids (r 0 > r 1 ), the answer is given in Ref. (9): optimize the value of t in (9). This gives…”

Section: Acute Pyramidsmentioning

confidence: 99%

“…Historically, for some time it was thought that the optimal measurement strategy for pyramidal states is the well-known square-root measurement (6) and even some security proofs for quantum cryptography were based on this reasonable conjecture (7,8). Recently, however, the optimality of the square-root measurement has been invalidated for a range of parameters of acute pyramids (9), and also for obtuse pyramids with three edges and very small volume (10). In this contribution, obtuse pyramids of any dimension are investigated, so that the optimal measurement strategies for pyramids of any shape and dimension is established.…”

Section: Introductionmentioning

confidence: 99%

How well can you know the edge of a quantum pyramid?

Englert

Řeháček

2010

Journal of Modern Optics

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We consider a symmetric quantum communication scenario in which the signal states are edges of a quantum pyramid of arbitrary dimension and arbitrary shape, and all edge states are transmitted with the same probability. The receiver could employ different decoding strategies: he could minimize the error probability, or discriminate without ambiguity, or extract the accessible information. We state the optimal measurement scheme for each strategy. For large parameter ranges, the standard square-root measurement does not extract the information optimally.Comment: 13 pages, 5 figures, 1 tabl

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“…We evaluate the extracted information by maximizing a success probability. Unfortunately, except two pure qubit 48 or particular case of pyramid state 70,71 , the analytic form of accessible information has not been known yet. In our work, we obtain the maximum of mutual information by a steepest-ascent method (The detailed analysis is given in the Method section) 72 .…”

Section: Resultsmentioning

confidence: 99%

Almost minimum error discrimination of N-ary weak coherent states by Jaynes-Cummings Hamiltonian dynamics

Namkung

Kwon

2019

Sci Rep

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Quantum state discrimination of coherent states has been one of important problems in quantum information processing. Recently, R. Han et al. showed that minimum error discrimination of two coherent states can be nearly done by using Jaynes-Cummings Hamiltonian. In this paper, based on the result of R. Han et al., we propose the methods where minimum error discrimination of more than two weak coherent states can be nearly performed. Specially, we construct models which can do almost minimum error discrimination of three and four coherent states. Our result can be applied to quantum information processing of various coherent states.

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Quantum cryptography: Security criteria reexamined

Cited by 11 publications

References 17 publications

Min-entropy and quantum key distribution: Nonzero key rates for “small” numbers of signals

Min-entropy and quantum key distribution: Nonzero key rates for “small” numbers of signals

How well can you know the edge of a quantum pyramid?

Almost minimum error discrimination of N-ary weak coherent states by Jaynes-Cummings Hamiltonian dynamics

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